Abstract
We find lower and upper bounds for the risk of estimating a manifold in Hausdorff distance under several models. We also show that there are close connections between manifold estimation and the problem of deconvolving a singular measure.
Citation
Christopher R. Genovese. Marco Perone-Pacifico. Isabella Verdinelli. Larry Wasserman. "Manifold estimation and singular deconvolution under Hausdorff loss." Ann. Statist. 40 (2) 941 - 963, April 2012. https://doi.org/10.1214/12-AOS994
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